Four decades ago, Leigh Van Valen presented the Red Queen's hypothesis to account for evolution of species within a multispecies ecological community [Van Valen L (1973) Evol Theory 1(1):1-30]. The overall conclusion of Van Valen's analysis was that evolution would continue even in the absence of abiotic perturbations. Stenseth and Maynard Smith presented in 1984 [Stenseth NC, Maynard Smith J (1984) Evolution 38(4):870-880] a model for the Red Queen's hypothesis showing that both Red-Queen type of continuous evolution and stasis could result from a model with biotically driven evolution. However, although that contribution demonstrated that both evolutionary outcomes were possible, it did not identify which ecological conditions would lead to each of these evolutionary outcomes. Here, we provide, using a simple, yet general population-biologically founded ecoevolutionary model, such analytically derived conditions: Stasis will predominantly emerge whenever the ecological system contains only symmetric ecological interactions, whereas both Red-Queen and stasis type of evolution may result if the ecological interactions are asymmetrical, and more likely so with increasing degree of asymmetry in the ecological system (i.e., the more trophic interactions, hostpathogen interactions, and the like there are [i.e., +/− type of ecological interactions as well as asymmetric competitive (−/−) and mutualistic (+/+) ecological interactions]). In the special case of no betweengenerational genetic variance, our results also predict dynamics within these types of purely ecological systems.coevolution | evolution within ecological communities | ecosystem structure | mathematical modeling | mathematical analysis T he major part of any species' environment is represented by the other (interacting) species in the ecosystem; hence, any evolutionary change made by any species within the ecosystem will, in general, be experienced as an environmental change by the coexisting species. This is the basis for the Red Queen's hypothesis as presented by Van Valen (1)-a proposition that is very similar to an idea suggested several decades earlier by Fisher (1930) (ref. 2, pp. 44-45) as well as Darwin (3). The Red Queen's hypothesis continues to attract much attention (3-10). However, within a multispecies ecological system it remains unclear whether evolution will cease or continue in the absence of external abiotic perturbations. Although the Darwinian theory of evolution provides a satisfactory explanation of the mechanisms for evolutionary changes and can be tested against short-term events, it does not in itself provide any predictions regarding large-scale and long-term features of the evolutionary dynamics. Essentially, we do not understand to what extent biotic factors (such as between-species interactions) are important determinants of macroevolution, or rather, what is the relative importance of biotic and abiotic processes in macroevolution (cf. ref. 11). To achieve such an understanding, we need to bring ecological and evoluti...